# 95% CI of A,C,E estimates in Twin model

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Joined: 05/18/2010 - 15:46
95% CI of A,C,E estimates in Twin model

Can anyone help me with the function or syntex needed to calculate the 95% CI for A,C,E estimates in the existing
UnivariateTwinAnalysis_MatrixRaw.R script.

Thanks in advance.

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Joined: 07/31/2009 - 15:14
See this part of the wiki:

See this part of the wiki: http://openmx.psyc.virginia.edu/wiki/mxCI-help

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Joined: 05/18/2010 - 15:46
Thanks for your help. I was

Thanks for your help. I was able to get the CI for A,C,E. I also would like to get the CI for standardized components ( e.g ACE.A/V,ACE.C/ACE.V,ACE.E/ACE.V). How do I compute it.

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Joined: 07/31/2009 - 15:14
Same way, just use the names

Same way, just use the names of the algebras instead of the names of the matrices in the list of elements for which you would like the CIs.

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Joined: 07/28/2016 - 16:42
Error in free[i, j] : subscript out of bounds

I tried various approaches to obtaining confidence intervals for a2, c2, and e2, but I always receive the same error message: "Error in free[i, j] : subscript out of bounds"

Can you please check what might be wrong with how I adjusted the UnivariateTwinAnalysis_PathRaw.R code (see below)? Or might there be a bug in the software version I'm running? Thanks!

data(twinData)

# Select Variables for Analysis

selVars <- c('bmi1','bmi2')
aceVars <- c("A1","C1","E1","A2","C2","E2")

# Select Data for Analysis

mzData <- subset(twinData, zyg==1, selVars)
dzData <- subset(twinData, zyg==3, selVars)

# Generate Descriptive Statistics

colMeans(mzData,na.rm=TRUE)
colMeans(dzData,na.rm=TRUE)
cov(mzData,use="complete")
cov(dzData,use="complete")
require(OpenMx)

# Path objects for Multiple Groups

manifestVars=selVars
latentVars=aceVars

# variances of latent variables

latVariances <- mxPath( from=aceVars, arrows=2,
+ free=FALSE, values=1 )

# means of latent variables

latMeans <- mxPath( from="one", to=aceVars, arrows=1,
+ free=FALSE, values=0 )

# means of observed variables

obsMeans <- mxPath( from="one", to=selVars, arrows=1,
+ free=TRUE, values=20, labels="mean" )

# path coefficients for twin 1

pathAceT1 <- mxPath( from=c("A1","C1","E1"), to="bmi1", arrows=1,
+ free=TRUE, values=.5, label=c("a","c","e") )

# path coefficients for twin 2

pathAceT2 <- mxPath( from=c("A2","C2","E2"), to="bmi2", arrows=1,
+ free=TRUE, values=.5, label=c("a","c","e") )

# covariance between C1 & C2

covC1C2 <- mxPath( from="C1", to="C2", arrows=2,
+ free=FALSE, values=1 )

# covariance between A1 & A2 in MZ twins

covA1A2_MZ <- mxPath( from="A1", to="A2", arrows=2,
+ free=FALSE, values=1 )

# covariance between A1 & A2 in DZ twins

covA1A2_DZ <- mxPath( from="A1", to="A2", arrows=2,
+ free=FALSE, values=.5 )

# Data objects for Multiple Groups

dataMZ <- mxData( observed=mzData, type="raw" )
dataDZ <- mxData( observed=dzData, type="raw" )

# Combine Groups

paths <- list( latVariances, latMeans, obsMeans,
+ pathAceT1, pathAceT2, covC1C2 )

mxMatrix(type="Full",nrow=3,ncol=1,free=T,values=.6,labels=c("a","c","e"),name="ace")
mxAlgebra( (ace%^%2) %x% solve(t(ace)%*%ace), name="StdVarComp",dimnames=list(c("a2","c2","e2"),NULL) )
mxCI("StdVarComp")

modelMZ <- mxModel(model="MZ", type="RAM", manifestVars=selVars,
+ latentVars=aceVars, paths, covA1A2_MZ, dataMZ, mxCI("StdVarComp"))
modelDZ <- mxModel(model="DZ", type="RAM", manifestVars=selVars,
+ latentVars=aceVars, paths, covA1A2_DZ, dataDZ )
minus2ll <- mxAlgebra( expression=MZ.fitfunction + DZ.fitfunction,
+ name="minus2loglikelihood" )
obj <- mxFitFunctionAlgebra( "minus2loglikelihood" )
modelACE <- mxModel(model="ACE", modelMZ, modelDZ, minus2ll, obj )

# Run Model

fitACE <- mxRun(modelACE, intervals=TRUE)
Error in free[i, j] : subscript out of bounds

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Joined: 03/01/2013 - 14:09
Error message has been improved

The message you got was not very helpful. In a more recent build, I got:

> fitACE <- mxRun(modelACE, intervals=TRUE)
Error: Unknown reference to 'StdVarComp' detected in a confidence interval specification in model 'ACE'
You should check spelling (case-sensitive), and also addressing the right model: to refer to an algebra
See help(mxCI) to see how to refer to an algebra in a submodel.
FYI, I got as far as: runHelper(model, frontendStart, intervals, silent, suppressWarnings, unsafe, checkpoint, useSocket, onlyFrontend, useOptimizer)

This clue was enough for me to figure out that some of the objects were missing from your model. Specifically, because the lines

mxMatrix(type="Full",nrow=3,ncol=1,free=T,values=.6,labels=c("a","c","e"),name="ace")
mxAlgebra( (ace%^%2) %x% solve(t(ace)%*%ace), name="StdVarComp",dimnames=list(c("a2","c2","e2"),NULL) )
mxCI("StdVarComp")

were not within the parentheses of an mxModel() function call, it could not find the objects to which the mxCI() referred. I modified the code to put the results of these commands into suitably named objects, and included these objects in the subsequent mxModel() call.

library(OpenMx)
# Load Data
data(twinData)

# Select Variables for Analysis
selVars <- c('bmi1','bmi2')
aceVars <- c("A1","C1","E1","A2","C2","E2")

# Select Data for Analysis
mzData <- subset(twinData, zyg==1, selVars)
dzData <- subset(twinData, zyg==3, selVars)

# Generate Descriptive Statistics
colMeans(mzData,na.rm=TRUE)
colMeans(dzData,na.rm=TRUE)
cov(mzData,use="complete")
cov(dzData,use="complete")
require(OpenMx)
# Path objects for Multiple Groups
manifestVars=selVars
latentVars=aceVars
# variances of latent variables
latVariances <- mxPath( from=aceVars, arrows=2,
free=FALSE, values=1 )
# means of latent variables
latMeans <- mxPath( from="one", to=aceVars, arrows=1,
free=FALSE, values=0 )
# means of observed variables
obsMeans <- mxPath( from="one", to=selVars, arrows=1,
free=TRUE, values=20, labels="mean" )
# path coefficients for twin 1
pathAceT1 <- mxPath( from=c("A1","C1","E1"), to="bmi1", arrows=1,
free=TRUE, values=.5, label=c("a","c","e") )
# path coefficients for twin 2
pathAceT2 <- mxPath( from=c("A2","C2","E2"), to="bmi2", arrows=1,
free=TRUE, values=.5, label=c("a","c","e") )
# covariance between C1 & C2
covC1C2 <- mxPath( from="C1", to="C2", arrows=2,
free=FALSE, values=1 )
# covariance between A1 & A2 in MZ twins
covA1A2_MZ <- mxPath( from="A1", to="A2", arrows=2,
free=FALSE, values=1 )
# covariance between A1 & A2 in DZ twins
covA1A2_DZ <- mxPath( from="A1", to="A2", arrows=2,
free=FALSE, values=.5 )

# Data objects for Multiple Groups
dataMZ <- mxData( observed=mzData, type="raw" )
dataDZ <- mxData( observed=dzData, type="raw" )

# Combine Groups
paths <- list( latVariances, latMeans, obsMeans,
pathAceT1, pathAceT2, covC1C2 )

aceMat <- mxMatrix(type="Full",nrow=3,ncol=1,free=T,values=.5,labels=c("a","c","e"),name="ace")
StdVarCompAlg <- mxAlgebra( (ace%^%2) %x% solve(t(ace)%*%ace), name="StdVarComp", dimnames=list(c("a2","c2","e2"),NULL) )
mxCI("StdVarComp")

modelMZ <- mxModel(model="MZ", type="RAM", manifestVars=selVars,
latentVars=aceVars, paths, covA1A2_MZ, dataMZ )
modelDZ <- mxModel(model="DZ", type="RAM", manifestVars=selVars,
latentVars=aceVars, paths, covA1A2_DZ, dataDZ )
minus2ll <- mxAlgebra( expression=MZ.fitfunction + DZ.fitfunction,
name="minus2loglikelihood" )
obj <- mxFitFunctionAlgebra( "minus2loglikelihood" )
modelACE <- mxModel(model="ACE", modelMZ, modelDZ, minus2ll, obj, aceMat, StdVarCompAlg, mxCI("StdVarComp"))

# Run Model
summary(fitACE <- mxRun(modelACE, intervals=TRUE))

The lower CI on the estimate of C which is already at zero sort of flunks out but could be considered to be zero.

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Joined: 07/21/2017 - 13:13
ran into the same problem

Hi,
I know this is an old thread, but I ran into the same problem and would like to ask for your help.
I have been trying to adjust this code to mine, in order to get the CI of the ACE standardized variance components (a2/V etc..).

This is what I added:

#Confidence interval for the variance components
aceMat <-mxMatrix(type="Full",nrow=3,ncol=1,free=T,values=StartVar.ACE,labels=c("a","c","e"),name="ace")
mxal <-mxAlgebra( (ace%^%2) %x% solve(t(ace)%*%ace), name="StdVarComp",dimnames=list(c("a2","c2","e2"),NULL) )
mxCI("StdVarComp")

obj <- mxFitFunctionMultigroup(c("MZM","DZM","MZF","DZF"))
modelACE.Homog <- mxModel(model="ACE_Homog",modelMZM, modelDZM,modelMZF, modelDZF, obj, aceMat,mxal, mxCI("StdVarComp") )

mxAutoStart(modelACE.Homog)
fitACE.Homog <- mxTryHardOrdinal(modelACE.Homog, intervals=TRUE)
sumACE.Homog <- summary(fitACE.Homog)

And I got the following message:
Error: The reference 'StdVarComp' does not exist. It is used by named reference 'confidence interval StdVarComp'

I am guessing that I have a simple syntax mistake, but cannot find it.
Do you have any idea what I did wrong?

Thank you very much

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Joined: 01/24/2014 - 12:15
I don't see anything wrong

I don't see anything wrong with your syntax. I'm curious what you get from

mxEval(StdVarComp, modelACE.Homog, TRUE)

and from

fitACE.Homog <- mxRun(modelACE.Homog, intervals=TRUE)

(i.e. using mxRun() instead of mxTryHardOrdinal() and without first using mxAutoStart()).

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Joined: 07/31/2009 - 14:25
To add to mikes reply: You

To add to mikes reply: You will need to create these standardizing algebras in your model, if they are not already present.

i.e., you can't just ask for mxCI("ACE.A/ACE.Vtot"), you have to create
mxAlgebra(ACE.A/ACE.Vtot, name="stdA")
mxCI(c('stdA')

On that note, wouldn't it be great if you could just include things in the mxCI statement and they would be automagically created!!

All the information is there.

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Joined: 05/18/2010 - 15:46
You spelled my wish.

You spelled my wish. Initially, I did try that way but it didn't work. Thanks a lot to both of you. It worked. Great help.

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Joined: 05/15/2014 - 02:26
Hi, I followed

Hi, I followed UnivariateTwinAnalysis_PathRaw.R instead of UnivariateTwinAnalysis_MatrixRaw.R.

I'm pretty new to OpenMx and R. Could anyone help me generate the 95%CI for standardized A, C, E? Thanks!

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Joined: 04/19/2011 - 21:00
Add algebras to your mxModel and request CIs for them

Do you want confidence intervals for the standardized path coefficients connecting the latent A, C, and E to the manifest variables? Or do you want confidence intervals for the standardized biometric variance components?

If you want them for the path coefficients, see my post in this other thread: http://openmx.psyc.virginia.edu/thread/2835 .

If you want them for the variance components, try adding something like the following to either your MZ-twin or DZ-twin submodel (it should not matter which):

mxMatrix(type="Full",nrow=3,ncol=1,free=T,values=.6,labels=c("a","c","e"),name="ace"),
mxAlgebra( (ace%^%2) %x% solve(t(ace)%*%ace), name="StdVarComp",dimnames=list(c("a2","c2","e2"),NULL) ),
mxCI("StdVarComp"),

I am assuming here that the single-headed paths going from the latent A, C, and E to the manifest variables are respectively labeled "a", "c", and "e", as in UnivariateTwinAnalysis_PathRaw.R . Also, depending on where in the mxModel() statement you put this code, you might need to delete that last comma. Then, when you use mxRun(), be sure to include argument intervals=TRUE. You can see the CIs in the output from summary(twinACEFit) or whatever.

What the code is doing is creating an mxMatrix to hold the path coefficients, because we're going to calculate something from them with an mxAlgebra, and algebras require matrices. What the algebra does is square each path coefficient, turning them into raw (unstandardized) variance components, and then divide them by the sum of their squares which is equal to the total phenotypic variance. The result is that raw variance components get divided by total variance, yielding standardized components--estimates of the phenotype's narrow-sense heritability, shared-environmentality, and unshared-environmentality.

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Joined: 05/15/2014 - 02:26
Thank you for solving my problem

What I want are the confidence intervals for the standardized biometric variance components (a2, c2, e2). My problem got solved after adding your script to the original file. The instruction is very helpful and clear. Thank you so much for your help.

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Joined: 04/19/2011 - 21:00
You're welcome. Glad to be

You're welcome. Glad to be of help.

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Joined: 02/19/2015 - 06:55
95% CI using bootstrap

I'm would like to get bootstrapped CI for my standardized path coefficients connecting the latent A, C, and E to the manifest variables, and to my standardized biometric variance components in a ACE model, defined using matrixes (I modified Neale's script (http://openmx.psyc.virginia.edu/thread/554) to add a further covariant, I couldn't figure it out using path definitions). Conventional 95% intervals won't work because of empirical under-identification. Is there an easier way then to run the model then taking bootstrapped samples and defining the mean and min max of the bootstrap distribution of the standardized path coefficients and variance components?

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Joined: 03/01/2013 - 14:09
mxBootstrap()

Yes, there's a recent implementation of bootstrapping in OpenMx, which avoids the model being interpreted repeatedly. See
?mxBootstrap
the function call looks like this:
mxBootstrap(model, replications=200, ...,
data=NULL, plan=NULL, verbose=0L,
parallel=TRUE, only=as.integer(NA),
OK=mxOption(model, "Status OK"), checkHess=FALSE)

I can't remember in which version this first appeared.

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Joined: 04/30/2018 - 08:34
CI estimation of univariate genetic model

I‘m new to OpenMx and R. I analyzed my twin data via UnivariateTwinAnalysis_PathRaw.R. However, the result didn't contain the 95%CI for a2,c2,e2 and Δχ2,p value of different models. Could anyone please tell me how to change the scripts to obtain these results.
I have added these codes to the above scripts ,

ci        <- mxCI(c("StPathA","StPathC","StPathE","PropVA", "PropVC", "PropVE",
"corA","corC","corE", "corP"))
CholAceModel  <- mxModel( "CholACE", pars, modelMZ, modelDZ, minus2ll, obj, ci )

# Run Cholesky Decomposition ACE model
CholAceFit    <- mxRun(CholAceModel, intervals=T)

But i still can't obtain that result I wanted.

File attachments:
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Joined: 01/24/2014 - 12:15
Concerning the change in

Concerning the change in -2logL between two models, you can directly pull the -2logL value from a model's output slot, e.g.

LL_ACE <- twinACEFit$output$fit

I can tell from your script that you already know how to calculate LRT statistics, but to get a p-value from each, use pchisq(), with the appropriate df and with argument lower.tail=FALSE.

Concerning confidence intervals: the first argument to mxCI() has to be a vector of character strings, with each string referring to a named entity--a labeled path or parameter, an MxMatrix, or an MxAlgebra--in the MxModel object's namespace. The call to mxCI() in your post does not reference any named entities in the namespace of MxModel twinACEModel. As has been stated previously in this thread, you'll need to create MxAlgebras that calculate the quantities of interest, put them into your MxModel, and request CIs for them. For instance, to get a CI for the raw and standardized additive-genetic variance components, create the followoing objects,

va <- mxAlgebra(a^2, "Va")
v <- mxAlgebra( (a^2)+(c^2)+(e^2), "Vp")
stva <- mxAlgebra( Va/Vp, "StVa")
ci <- mxCI(c("Va","StVa"))

, and put them into your MZ or DZ submodel (it should not matter which).

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Joined: 03/01/2013 - 14:09
Yep, and mxCompare()

A simpler and more direct way to obtain a table of results including LRT deltas and p values is to use mxCompare(baseFittedModel, comparisonFittedModel).

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Joined: 04/30/2018 - 08:34
P value

Thank you very much. You really gave me great help.The last problem for me about this scripts is to get a p-value from each model. You have told me to" use pchisq(), with the appropriate df and with argument lower.tail=FALSE." Because I really know little about R, could please give me an example in this scritps :

#  AE model
# path coefficients for twin 1
pathAceT1    <- mxPath( from=c("A1","C1","E1"), to=selVars[1], arrows=1,
free=c(T,F,T), values=c(.6,0,.6),  label=c("a","c","e") )
# path coefficients for twin 2
pathAceT2    <- mxPath( from=c("A2","C2","E2"), to=selVars[2], arrows=1,
free=c(T,F,T), values=c(.6,0,.6),  label=c("a","c","e") )

# Combine Groups
paths        <- list( latVariances, latMeans, obsMeans,
pathAceT1, pathAceT2, covC1C2 )
aceMat <- mxMatrix(type="Full",nrow=3,ncol=1,free=T,values=.5,labels=c("a","c","e"),name="ace")
StdVarCompAlg <- mxAlgebra( (ace%^%2) %x% solve(t(ace)%*%ace), name="StdVarComp", dimnames=list(c("a2","c2","e2"),NULL) )
mxCI("StdVarComp")
modelMZ      <- mxModel(model="MZ", type="RAM", manifestVars=selVars,
latentVars=aceVars, paths, covA1A2_MZ, dataMZ )
modelDZ      <- mxModel(model="DZ", type="RAM", manifestVars=selVars,
latentVars=aceVars, paths, covA1A2_DZ, dataDZ )
minus2ll     <- mxAlgebra( expression=MZ.fitfunction + DZ.fitfunction,
name="minus2loglikelihood" )
obj          <- mxFitFunctionAlgebra( "minus2loglikelihood" )
modelAE <- omxSetParameters(model=ACEFit,labels="c",free=FALSE,values=0,name="AE")
# Run Model
AEFit    <- mxRun(modelAE,intervals=TRUE)
AESum    <- summary(AEFit)
# Fit AE model
# -----------------------------------------------------------------------------

# Generate & Print Output
M  <- mxEval(mean, AEFit)
A  <- mxEval(a*a, AEFit)
C  <- mxEval(c*c, AEFit)
E  <- mxEval(e*e, AEFit)
V  <- (A+C+E)
a2 <- A/V
c2 <- C/V
e2 <- E/V
estAE <- rbind(cbind(A, C, E),cbind(a2, c2, e2))
LL_AE <- mxEval(fitfunction, AEFit)
LRT_ACE_AE <- LL_AE - LL_ACE

estACE
estAE
LRT_ACE_AE
# Get Model Output
# -----------------------------------------------------------------------------

# AE model details

AESum
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Joined: 01/24/2014 - 12:15
ProTip: It's a good idea to

ProTip: It's a good idea to look at the help page for an R function that's unfamiliar to you before you use it. You can see the help page by entering the function symbol, preceded by a question mark, at the R prompt, e.g. ?pchisq.

Concerning your script in particular, try this:

pchisq(q=LRT_ACE_AE,df=1,lower.tail=FALSE)

The df=1 is because there is a difference of 1 in the number of free parameters in the ACE model versus the AE model. This command will give you the p-value for the test of the null hypothesis that C variance is zero (when both A variance and E variance are free).

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Joined: 03/01/2013 - 14:09
mxCompare too

Rob's code works. Simpler to use, however, would likely be the mxCompare() function, to which you pass a model and a submodel and it works out the likelihood ratio test and p-value for you. Again ?mxCompare documentation is a good place to start.

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Joined: 04/30/2018 - 08:34
CI estimation of univariate genetic model

I have change my scripts to this:

# Combine Groups
paths        <- list( latVariances, latMeans, obsMeans,
pathAceT1, pathAceT2, covC1C2 )

aceMat <- mxMatrix(type="Full",nrow=3,ncol=1,free=T,values=.5,labels=c("a","c","e"),name="ace")
StdVarCompAlg <- mxAlgebra( (ace%^%2) %x% solve(t(ace)%*%ace), name="StdVarComp", dimnames=list(c("a2","c2","e2"),NULL) )
mxCI("StdVarComp")

modelMZ      <- mxModel(model="MZ", type="RAM", manifestVars=selVars,
latentVars=aceVars, paths, covA1A2_MZ, dataMZ )
modelDZ      <- mxModel(model="DZ", type="RAM", manifestVars=selVars,
latentVars=aceVars, paths, covA1A2_DZ, dataDZ )
minus2ll     <- mxAlgebra( expression=MZ.fitfunction + DZ.fitfunction,
name="minus2loglikelihood" )
obj          <- mxFitFunctionAlgebra( "minus2loglikelihood" )

modelACE <- mxModel(model="ACE", modelMZ, modelDZ, minus2ll, obj, aceMat, StdVarCompAlg, mxCI("StdVarComp"))

# Run Model

ACEFit   <- mxRun(modelACE,intervals=TRUE)
ACESum   <- summary(ACEFit)
ACESum

Then, I obtained the CI for ACE. However, when I used the same scripts to run AE model as this:

# Combine Groups
paths        <- list( latVariances, latMeans, obsMeans,
pathAceT1, pathAceT2, covC1C2 )
aceMat <- mxMatrix(type="Full",nrow=3,ncol=1,free=T,values=.5,labels=c("a","c","e"),name="ace")
StdVarCompAlg <- mxAlgebra( (ace%^%2) %x% solve(t(ace)%*%ace), name="StdVarComp", dimnames=list(c("a2","c2","e2"),NULL) )
mxCI("StdVarComp")
modelMZ      <- mxModel(model="MZ", type="RAM", manifestVars=selVars,
latentVars=aceVars, paths, covA1A2_MZ, dataMZ )
modelDZ      <- mxModel(model="DZ", type="RAM", manifestVars=selVars,
latentVars=aceVars, paths, covA1A2_DZ, dataDZ )
modelAE <- mxModel(model="AE", modelMZ, modelDZ, minus2ll, obj, aceMat, StdVarCompAlg, mxCI("StdVarComp"))

an error happened:

> # Run Model
> AEFit    <- mxRun(modelAE,intervals=TRUE)
Error: In model 'AE' the name 'c' is used as a free parameter in 'AE.ace' and as a fixed parameter in 'MZ.A' and 'DZ.A'

I don't know how to solve the question, could anyone can help me?

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Joined: 01/24/2014 - 12:15
omxSetParameters()

There's no need to reconstruct a new MxModel object from its constituent parts just to fix the shared-environmental variance to zero. Just do

modelAE <- omxSetParameters(model=ACEfit,labels="c",free=FALSE,values=0,name="AE")

and proceed.

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Joined: 04/30/2018 - 08:34
modelE

Thank you very much. I have obtained the result of ACE,AC&CE. However, when I change:
modelE <- omxSetParameters(model=ACEFit,labels="a",labels="c",free=FALSE,values=0,name="E")
There was an error:
Error in omxSetParameters(model = ACEFit, labels = "a", labels = "c", :
formal argument "labels" matched by multiple actual arguments
Could u please help me rewrite the scripts to get the result of E model?

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Joined: 01/24/2014 - 12:15
c() is your friend

This,

modelE <- omxSetParameters(model=ACEFit,labels="a",labels="c",free=FALSE,values=0,name="E")

isn't valid R syntax. You can't pass two different values for one function argument specified by name like that. What you want to do instead is

modelE <- omxSetParameters(model=ACEFit,labels=c("a","c"),free=FALSE,values=0,name="E")

. The function c() is for concatenating multiple values into a vector.

It would also work to fix the two free parameters via two calls to omxSetParameters():

modelE <- omxSetParameters(model=ACEFit,labels="a",free=FALSE,values=0,name="E")
modelE <- omxSetParameters(model=modelE,labels="c",free=FALSE,values=0)

That's a bit inelegant, though.

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Joined: 04/30/2018 - 08:34
Thank you for your help

It's very lucky for me to find this forum. Rob and Neale are so nice!
Best wishes to you!